PRIVATE COLLECTIONS

James Stirling: Mathematician of the Newtonian Age

29 September 2025

Dominic Somerville-Brown

We are proud to present The Library of James Stirling, Mathematician a private collection to be offered at auction on 23 October 2025.

James Stirling was born on 11 May 1692 at Garden House, near Stirling, Scotland, the third son of Jacobite laird Archibald Stirling, who had been acquitted of high treason for his role in the Brig o’Turk gathering of 1708, and his second wife. He was to become one of the leading mathematicians in Europe in the early 18th century, cultivating relationships with Sir Isaac Newton, Colin Maclaurin, Gabriel Cramer and Leonhard Euler among others. He made a valuable contribution in the fields of infinitesimal calculus and infinite series, and gives his name to the Stirling numbers and to Stirling’s formula.

The Library of James Stirling, Mathematician

Browse our 23 October auction online now.

The Library of James Stirling | In Discussion

Join our Head of Rare Books & Manuscripts Cathy Tait and Dr Michael Barany, Historian of Science and Mathematics, University of Edinburgh as they discuss the life and work of James Stirling.

Little is known of Stirling’s early life until his arrival at Oxford in 1710. Coming from a Jacobite family, he matriculated as a non-juror in inauspicious circumstances which he reported in a letter home, informing his father that he had avoided taking the oath of allegiance "with the help of my tutor … but with much ado". In 1715 John Keill noted in a letter to Newton that the problem of orthogonal trajectories proposed by Leibniz had recently been solved by "Mr. Stirling an under-graduate here". His first book, Lineae tertii ordinis Neutonianae, a commentary on Newton's classification of cubic curves, was printed at the Sheldonian Theatre in April 1717, with Newton named as a subscriber.

Sir Isaac Newton

Analysis per quantitatum series, fluxiones, ac differentias

First edition, James Stirling's copy of this major collection of Newton's mathematical writings, published with the intention of establishing his priority over Leibniz in the discovery of calculus, the controversy then being at its height. Edited by Welsh mathematician William Jones, it contains the first editions of two foundational works.

£40,000 - 60,000 + fees

By that time Stirling's status as a non-juring student and his alleged involvement in Jacobite agitation had already led to trouble with the university authorities, and his scholarships appear to have been withdrawn shortly before the book was published. He therefore left Oxford without a degree, taking up an invitation to Venice from Nicolas Tron, the Venetian ambassador to London. Stirling was in Italy for several years, and became known in his family as ‘the Venetian’ in consequence. During this time Stirling attended the university of Padua and made the acquaintance of scholars including Nicolaus Bernoulli. In 1719 he wrote to Newton from Venice thanking him for an unspecified act of generosity, usually interpreted as a gift of money, and in the same year communicated to the Royal Society his paper ‘Methodus differentialis Newtoniana illustrata’, the basis for his magnum opus, the Methodus differentialis sive tractatus de summatio et interpolatio serierum infinitarum, which was published in 1730. Stirling’s holograph manuscript of the Methodus, his corrected copy of the first edition, and a copy of the first edition in English are all present in his library.

James Stirling (1692-1770)

'Methodus Differentialis sive Tractatus de Summatione et Interpolatione Serierum Infinitarum'

author's holograph manuscript, c.1730

James Stirling's holograph manuscript of his masterpiece and ‘principal contribution to mathematics' (ODNB), which introduced the Stirling numbers and Stirling's formula

£40,000 - 60,000 + fees

Stirling was back in Scotland by 1722, and in 1725 became a tutor at Watts’s Academy in Little Tower Street, Covent Garden. The following year he was elected to the Royal Society, and his surviving correspondence shows that he spent the ensuing decade engaged in the productive exchange of ideas with his peers across Europe as the Newtonian revolution unfolded, while calling regularly on the aged Newton himself, informing his brother in a letter home that "Sr Isaac Newton lives a little way of in the country. I go frequently to see him, and find him extremely kind and serviceable in every thing I desire, but he is much failed and not able to do as he has done". He also developed a special interest in the debate on the shape of the Earth and the resulting distribution of its gravitational forces, publishing an important essay to the subject in the Philosophical Transactions. Weights and measures became another area of research.

Sr Isaac Newton lives a little way of in the country. I go frequently to see him, and find him extremely kind and serviceable in every thing I desire, but he is much failed and not able to do as he has done’

James Stirling on his visits to Sir Isaac Newton

In 1735 James Stirling was appointed manager of the mines at Leadhills, Lanarkshire on behalf of the Scots Mining Company. Records of this period show that Stirling restored the commercial fortunes of the mines, regularised and improved the working conditions of the miners, and introduced technological innovations including a ventilation system for mine shafts and furnaces. At Leadhills Stirling found he had less time than we wished for mathematical research, and this may have deterred him from accepting the offer of the Edinburgh University chair in mathematics following the death of Maclaurin in 1746. By this period his energies were devoted mainly to the application of scientific knowledge: his survey of the River Clyde, conducted in 1752 on behalf of the Corporation of Glasgow, helped establish the city as a major commercial and imperial centre.

James Stirling married late in life, probably after 1745. His wife Barbara Watson died in 1753. Their one daughter, Christian, married her cousin Archibald Stirling, the heir to the family estate and James’s successor as manager of Leadhills.

Colin Maclaurin (1698-1746)

Ten autograph letters signed to James Stirling

A major collection of letters illuminating the working relationship of two leading lights of the Newtonian revolution, and two of the most important Scottish mathematicians of any era.

£15,000 - 20,000 + fees

Department

Books & Manuscripts

About the Author

Specialist

Dominic Somerville-Brown

Books & Manuscripts Specialist | Edinburgh

dsb@lyonandturnbull.com

0131 557 8844